See http://illumos.org/hcl for a correct list of supported hardware (based on device IDs the actual drivers list as supported)

The bge driver now supports Broadcom BCM5719/5720 devices. See Illumos bug# 3446 for more details.

A number of NICs are not currently supported "out of the box" by the illumos kernel or OpenIndiana distribution, but over 30 open-sourced drivers covering many more chipsets and NIC models are available as part of the separate "Free NIC drivers for OpenSolaris" projectby Masayuki Murayama and generally do just work on OpenIndiana (binaries are available as part of the source code tarballs, but you're encouraged to recompile them with GLDv3 Makefile's on OpenIndiana, see details on the project's web page). If your newer NIC chipset is not supported by a driver from that project, try contacting the author - you might help him make and test an updated version of a driver